In return, the DUP will support the Government in all votes on the Budget and everything to do with Brexit, making it easier for the Prime Minister to have her way on Britain's negotiating strategy with Europe.

But the Conservatives will still have to battle to pass other laws, striking deals with the DUP on a case-by-case basis.

Theresa May and Arlene Foster met with their deputies and senior MPs at Number 10 to seal the deal around the Cabinet table.

The PM and DUP boss watched as Chief Whip Gavin Williamson and top Unionist Jeffrey Donaldson both formally signed the agreement.

Mrs Foster said she was "delighted" by the conclusion of talks, while Mrs May added that the parties "share many values" and said the agreement was "a very good one".

But Labour leader Jeremy Corbyn said the deal was "not in the national interest".

He said today: "Austerity has failed. Cuts to vital public services must be halted right across the UK, not just in Northern Ireland.

"The Government must immediately answer two questions. Where is the money for the Tory-DUP deal coming from? And, will all parts of the UK receive the much needed additional funding that Northern Ireland will get as part of the deal?

"This Tory-DUP deal is clearly not in the national interest but in May's party's interest to help her cling to power."

The two leaders today struck a deal on a confidence and supply agreement

Speaking in No 10, Mrs May said: "As we set out at the beginning of the talks, we share many values in terms of wanting to see prosperity across the UK, the value of the union, the important bond between the different parts of the United Kingdom.

"We very much want to see that protected and enhanced and we also share the desire to ensure a strong government, able to put through its programme and provide for issues like the Brexit negotiations, but also national security issues.

"So the agreement we have come to is a very, very good one, and look forward to working with you."

Mrs Foster added: "We're delighted that we have reached this agreement, which I think works, obviously, for national stability."

The deal is supposed to last "for the length of the Parliament" but it will be reviewed by both parties "after each parliamentary session" - i.e. in two years' time.

In addition, much of the additional funding is valid for just two years - raising the possibility that Mrs May will call another General Election in 2019, when Britain has finished the process of quitting the EU.

The DUP boss was keen to strike a deal before Thursday's vote on the Queen's Speech

The Government says that the additional payments will count as "grants" rather than regular spending - which allows ministers to avoid having to spend extra money on Scotland and Wales.

It was previously feared that the deal would trigger the "Barnett formula" which fixes the relative amount of funding received by the four nations of the UK, forcing the Tories to hand over billions more to Cardiff and Edinburgh.

Wales's first minister Carwyn Jones slammed the agreement as a "straight bung", while Nicola Sturgeon said: "Any sense of fairness sacrificed on the altar of grubby DUP deal to let PM cling to power."

Nigel Dodds, the DUP deputy leader, mocked the opposition parties' supposed anger at the deal with the Tories.

He said in the House of Commons: "Some day I'd like to think we might publish all of the correspondence and conversations we had in 2010 with the Labour front bench and in 2015 with the Labour front bench, and indeed with the SNP as well.

"Because some of the faux outrage we have heard is hypocrisy of the highest order."

Theresa May faces a vote of confidence in the form of the Queen's Speech debate

Chris Patten warned yesterday that the Tory-DUP tie-up risked making the Conservatives into the "nasty party" again.

Echoing comments made recently by John Major, the ex-minister said: "The DUP is a toxic brand."

Former Deputy PM Michael Heseltine said the Government would be at risk of collapse within two years.

He told BBC Radio 4's World At One today: "This is a deeply divided country and singling out one part of it in order to give a semblance of short-term stability is just one more of the prices we are paying for the consequences of Brexit.

"I think it will take two years, 18 months, for the Government to be at risk, and that's assuming they can command the loyalty in the Brexit confrontations of every Conservative MP."

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But David Cameron today spoke out in support of the deal, saying Mrs May was right to team up with the Unionists.

He wrote on Twitter: "Task facing PM, given the circs, is to deliver the most stable govt possible - today's DUP deal helps achieve that. All Cons should support."

First Secretary of State Damian Green said the Conservatives "could have" continued without signing the deal but insisted that it would give voters "more confidence" in the stability of the Government.

Grant Shapps, the former Tory chairman, joked that the party would have won a "stonking majority" if it had ditched its unpopular welfare policies before the election, rather than now.

The Irish government cautiously welcomed the deal, suggesting it could help prevent a hard border between Northern Ireland and the Republic after Brexit.

Foreign minister Simon Coveney said: "An enhanced Northern Ireland voice articulating an agreed devolved government position could see more effective and inclusive representation of the unique circumstances of Northern Ireland at Westminster."

As well as talks with the Conservatives, the DUP faces a deadline this week for negotiations over power-sharing in Northern Ireland.

Mrs Foster said: "I very much hope that this week we will be able to conclude on two agreements."

The Northern Irish Assembly has been suspended for months in the wake of a scandal over energy subsidies.